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Journal ArticleDOI

Thin elastic and periodic plates

TLDR
In this article, a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small is studied and convergence proof is carried out.
Abstract
This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e 0 then ω 0), (ω 0 then e 0) and lately (e and ω 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.

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Citations
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Journal ArticleDOI

A new model for thin plates with rapidly varying thickness

TL;DR: In this paper, the bending of a thin plate with rapidly varying thickness was studied and a fourth-order equation for the midplanc displacement was derived using an asymptotic analysis based on 3D linear elasticity.
Journal ArticleDOI

Asymptotic Homogenization of Composite Materials and Structures

TL;DR: In this article, a review of the state-of-the-art in asymptotic homogenization of composites is presented, by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications.
Journal ArticleDOI

Homogenization of corrugated core sandwich panels

TL;DR: In this paper, the effective properties of corrugated core sandwich panels are investigated, based on the asymptotic expansion method, and an equivalent Reissner-Mindlin homogeneous plate is derived.
References
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Journal ArticleDOI

A justification of a nonlinear model in plate theory

TL;DR: In this article, the first term in the expansion is a solution of a known bi-dimensional model in nonlinear plate theory, and the existence of the second term is also established.
Journal ArticleDOI

Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory

TL;DR: In this article, the eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2 ϵ, are shown to converge (in a specific sense) to the 2-dimensional biharmonic operator of plate theory, as ϵ approaches zero.